It could be about Naruto having some sort of connection to Pain. Maybe in this fanfiction, Naruto is somehow related to Pain in a way that wasn't in the original story, like being his son in an alternate universe. This could lead to a whole new set of storylines, with Naruto perhaps having to deal with the legacy of Pain while also following his own path as a ninja.
In many fanfictions, Naruto might use new jutsus or a deeper understanding of his own power. Maybe he taps into a more powerful form of the Nine - Tails' chakra and combines it with his Sage Mode in a unique way to overpower Pain.
I'm not sure specifically as there could be many different takes in a fanfic with that title. It might be about a character in Naruto who endures some sort of unending pain, perhaps related to their past traumas, like Naruto himself who has the pain of being an orphan and ostracized for so long. Or it could be about a villain like Sasuke who has his own internal pain that never seems to go away.
In some fanfictions, Naruto's pain might manifest through his actions. For example, he could become withdrawn and isolate himself from his friends. This is because Naruto has always been a social person, so any deviation from his normal behavior could be a sign of his internal pain.
One possible cause could be his sense of failure. Naruto always wants to protect his friends and village, so if he fails in a mission or is unable to save someone, it can cause him great pain.
In such a fanfic, it might explore the emotional turmoil. Pain's attacks on the village would not only be a physical threat but also an emotional one. Hinata could be in a position where she has to choose between her love for Naruto and her duty to the village. Naruto, on the other hand, would be dealing with his own feelings for Hinata while trying to defeat Pain. And Pain himself could be presented with more complex motives, perhaps having some sort of connection to Naruto's past that is revealed during the battle.
Since I haven't read this particular 'naruto it's better to share the pain fanfic', it's hard to say for sure. However, in the Naruto series, pain is a common theme. It could be that the fanfic explores how the characters deal with the pain of war, loss of loved ones, or the weight of their own abilities. Maybe it shows characters like Sasuke, who has his own share of pain from his clan's massacre, and Naruto working together to share and overcome their combined pain in ways that the original series didn't fully explore.
Here's how a fanfic might go. After the battle with Pain, Naruto is surrounded by people, but his eyes keep searching for Hinata. When he finally spots her, he makes his way through the crowd. Hinata is blushing but stands her ground. Naruto reaches her and says, 'Thank you for always being there for me.' Then, he cups her face and kisses her. This kiss is a culmination of all the times Hinata has supported Naruto, and now he's finally realizing his own feelings for her.
His fighting style could become more aggressive. Without the fear of pain, he might be willing to use more extreme techniques that would otherwise be too dangerous because of the pain they cause to the user. He could push his body to the limit more often.
Konan could be really interesting. In some fanfictions, she might have a different backstory or motivation that affects the Naruto vs Pain fight. For example, she could be secretly trying to stop Pain from going too far in his destruction of the Leaf Village.